6 papers · 1 filter
Smooth Realizations of Line Configurations
Paolo Aceto, Duncan McCoy, JungHwan Park
We study the problem of realizing line configurations as collections of 2-spheres smoothly embedded in the complex projective plane. Building upon prior work by Ruberman and Starks…
Topological line arrangements with high multiplicities
Paolo Aceto, Marco Golla
We investigate constraints on the existence of topological and smooth realisations of combinatorial line arrangements and -configurations in the complex projective plane. By…
Isotopy and equivalence of knots in 3-manifolds
Paolo Aceto, Corey Bregman, Christopher W. Davis +2
We show that in a prime, closed, oriented 3-manifold M, equivalent knots are isotopic if and only if the orientation preserving mapping class group is trivial. In the case of irred…
Handle decomposition complexity and representation spaces
Paolo Aceto, Aliakbar Daemi, Jennifer Hom +2
We prove that there are homology three-spheres that bound definite four-manifolds, but any such bounding four-manifold must be built out of many handles. The argument uses the homo…
A survey on embeddings of 3-manifolds in definite 4-manifolds
Paolo Aceto, Duncan McCoy, JungHwan Park
This article presents a survey on the topic of embedding 3-manifolds in definite 4-manifolds, emphasizing the latest progress in the field. We will focus on the significant role pl…
Definite fillings of lens spaces
Paolo Aceto, Duncan McCoy, JungHwan Park
This paper considers the problem of determining the smallest (as measured by the second Betti number) smooth negative-definite filling of a lens space. The main result is to classi…